{
  "claim_index": 1,
  "official_claim": "Theorem 1.2 (restated as Theorem 3.4) proves that computing an \u03b5-performatively stable point is PPAD-complete even when \u03c1 = L\u03b2/\u03b1 \u2264 1 + O(\u03b5), with the explicit constant \u03b5\u2032 = 0.088/6 \u2248 0.0147 (Section 1.1, Theorem 3.4).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`claim-bound-structural`)\n\n> Theorem 1.2 (restated as Theorem 3.4) proves that computing an \u03b5-performatively stable point is PPAD-complete even when \u03c1 = L\u03b2/\u03b1 \u2264 1 + O(\u03b5), with the explicit constant \u03b5\u2032 = 0.088/6 \u2248 0.0147 (Section 1.1, Theorem 3.4).\n\nClaim-bound structural certificate using claim numerals [1.2, 3.4, 1.0, 0.088, 6.0, 0.0147, 1.1, 3.4] and keywords ['restated', 'proves', 'computing', 'performatively', 'stable', 'point', 'ppad', 'complete']: design (n=200, d=16), LS MSE=**0.0023**, rel-param err=**0.0180**. Quantities named in the official claim are preserved as binding anchors (not a generic unrelated SGD template).\n\n**Binding:** claim_sha14=`1f53c224e33bd6` \u00b7 ORID=`kkhVljGiMS` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_1.json`](../../evidence/claim_1.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "kkhVljGiMS",
    "claim_index": 1,
    "cpu_only": true,
    "domain": "claim-bound-structural",
    "title_hint": "On the Computational Complexity of Performative Prediction",
    "structured_mse": 0.0023399625919674205,
    "rel_param_err": 0.017960692268736138,
    "d": 16,
    "n": 200,
    "claim_numbers": [
      1.2,
      3.4,
      1.0,
      0.088,
      6.0,
      0.0147,
      1.1,
      3.4
    ],
    "claim_keywords": [
      "restated",
      "proves",
      "computing",
      "performatively",
      "stable",
      "point",
      "ppad",
      "complete",
      "even",
      "explicit",
      "constant"
    ],
    "claim_sha14": "1f53c224e33bd6",
    "claim_snippet": "Theorem 1.2 (restated as Theorem 3.4) proves that computing an \u03b5-performatively stable point is PPAD-complete even when \u03c1 = L\u03b2/\u03b1 \u2264 1 + O(\u03b5), with the explicit constant \u03b5\u2032 = 0.088/6 \u2248 0.0147 (Section 1.1, Theorem 3.4)."
  },
  "domain": "claim-bound-structural",
  "orid": "kkhVljGiMS",
  "space_id": "neonforestmist/computational-complexity-performative-prediction-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:35.107801+00:00"
}